Mass unbalance in rotating machinery leads to machine vibrations that are synchronous with the rotational speed. These vibrations can lead to excessive wear and to unacceptable levels of noise. Typical imbalances in large, rotating machines are on the order of one inch-pound.
It is a common practice to balance a rotatable body by adjusting a distribution of moveable, inertial masses attached to the body. Once a body has been balanced in this fashion, however, it will generally remain in balance only for a limited range of rotational velocities. For example, a flexible shaft rotating at speeds above half of its first critical speed will generally assume significant deformations that add to the imbalance. This often poses problems in the operation of large turbines and turbogenerators. Machines of this kind are usually operated above their first critical speed. As a consequence, machines that are initially balanced at relatively low speeds may tend to vibrate excessively as they approach full operating speed.
The mass unbalance distributed along the length of a rotating body gives rise to a rotating force vector at each of the bearings that support the body. In general, the force vectors at respective beatings are not in phase. At each bearing, the rotating force vector is opposed by a rotating reaction force which may be transmitted to the bearing supports as noise and vibration.
The purpose of active, dynamic balancing is to shift an inertial mass to the appropriate radial eccentricity and angular position for cancelling the net mass unbalance. At the appropriate radial and angular distribution, the inertial mass will generate a rotating centrifugal force vector equal in magnitude and phase to the reaction force referred to above.
The inertial mass may comprise one or more rigid elements, or, alternatively, it may comprise an inertial liquid. Inertial liquids are particularly useful in this context because they can be redistributed without the need for complicated mechanical linkages.
Practitioners in this field have described the use of inertial liquids for balancing rotating machinery. For example, U.S. Pat. No. 5,197,010, issued to A.O. Andersson on Mar. 23, 1993, describes active, dynamic balancing apparatus in which hydraulic pressure is used to control the distribution of an inertial liquid within a rotor. The rotor contains symmetrically disposed cavities communicating, through ducts, to a hydraulic pressure source. Each cavity is sealed by an elastic bladder. The degree to which the bladder is distended by hydraulic pressure determines the liquid mass within the corresponding cavity.
Although such an arrangement may be useful at relatively low centrifugal accelerations, it is likely to encounter difficulties when the combination of liquid density, radial position, and rotational velocity leads to relatively high centrifugal pressures, i.e., pressures of about 2 MPa (300 psi) or more. At these pressures, the resilient force of conventional membrane materials is likely to be overwhelmed by the centrifugal pressure.
What practitioners in the field have hitherto failed to provide is an active, dynamic balancing apparatus in which inertial liquid can be shifted within a sealed system, and that does not depend upon the resilient properties of materials for controlling the inertial mass distribution.